Problem: Rewrite as a simplified fraction. ${2.14\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2143.3333...\\ 100x &= 214.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1929}$ ${x = \dfrac{1929}{900}} $ ${x = \dfrac{643}{300}} \text{or} {2 \dfrac{43}{300}}$